Algebra Se Paheliyaan Suljhao | Class 8 Maths Book 2 Ch 6

📘 Class 8 · Ganita Prakash Book 2Ch 6 · Algebra PlayPost 7 / 7⏱ 25–30 min

Algebra Se Paheliyaan Suljhao 🧞

IS POST MEIN

Pehle Yeh Aata Hai?Kahani Concept Deep Concept Examples Real Life Galti 10 MCQs FAQs Practice HOTS Olympiad Recap

✅ Pehle Yeh Aata Hai?

Yeh post shuru karne se pehle, in teen sawaalon ko 1 minute mein khud try kijiye:

2x = 14 → x?
5d + 6 = 3(d + 6) → d?
4h + 2(55 − h) = 150 → h?

Answers dekho

Teeno sahi? Aap paheliyon ke liye taiyaar ho! Equations yaad karni hon to Book 1 Ch 6 dekho.

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🎬 Kahani: Karim Aur Jinn

Karim ko ek jinn mila: “Bargad ke ped ka ek chakkar lagao, tumhare sikke double ho jaayenge! Bas har chakkar ke baad mujhe 8 sikke dena.”

Karim khush, teen chakkar lagaaye… aur aakhir mein uske paas ek bhi sikka nahi bacha! 😱 Shuru mein uske paas kitne sikke the?

Aaj algebra ke saath paheliyon ka safar!

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📖 Concept: Kahani Ko Equation Mein Badlo

Step 1: Karim aur jinn

Shuru = x. Chakkar 1: 2x − 8. Chakkar 2: 2(2x − 8) − 8 = 4x − 24. Chakkar 3: 8x − 56 = 0 → x = 7. Check: 14 − 8 = 6, 12 − 8 = 4, 8 − 8 = 0 ✅

Karim kab faayde mein? Kharcha c ho to aakhir 8x − 7c. Shuru se zyada tab jab 8x − 7c > x, yaani c < x. Jinn sab le jaaye: c = 8x ÷ 7.

Step 2: Phool aur teen mandir

Ek aadmi ke phool har talaab mein double hote hain; teen mandiron mein barabar phool rakhta hai, aakhir mein kuch nahi bachta. x phool, har mandir s: 2x − s → 4x − 3s → 8x − 7s = 0 → 8x = 7s. Sabse chhota: x = 7, s = 8.

Step 3: Sir aur pair

Ghode aur murgiyaan: 55 sir, 150 pair. Bina letter: sab murgi maano → 110 pair. 40 pair kam; har ghoda 2 extra pair → 20 ghode, 35 murgiyaan. Algebra: 4h + 2(55 − h) = 150 → h = 20 ✅

Step 4: Umar aur gaayein

Maa beti ki 5 guna; 6 saal baad 3 guna: 5d + 6 = 3(d + 6) → d = 6 (maa 30).
Naina ke paas Gauri se double gaayein; Naina 3 de to barabar: 2G − 3 = G + 3 → G = 6, N = 12.

Step 5: Dosa ki gaadi

Kiraya ₹5000/din, har dosa ki laagat ₹10. 100 dosa bech ke ₹2000 munafa: aamdani = 5000 + 1000 + 2000 = 8000 → ₹80 per dosa. ₹50 mein: (50 − 10)n = 7000 → n = 175.

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🔐 Deep Concept: 1/3 Ka Chhupa Pattern

1/3, (1 + 3)/(5 + 7) = 4/12, (1 + 3 + 5)/(7 + 9 + 11) = 9/27: sab 1/3!

Kyun? Pehle n odd numbers ka jod n². Pehle 2n ka jod (2n)² = 4n². To agle n ka jod = 4n² − n² = 3n². Bhaag = n² ÷ 3n² = 1/3. Hamesha! (Ch 2 ka odd numbers wala niyam phir kaam aaya.) 🔐

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✏️ Solved Examples

Example 1 (Easy): Sir 20, pair 56 (ghode aur murgiyaan). Ghode?

Sab murgi: 40 pair. 16 extra ÷ 2 = 8 ghode, 12 murgiyaan.

WHY sahi hai? 8 × 4 + 12 × 2 = 56 ✅

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Example 2 (Medium): Baap bete se 4 guna; 5 saal baad 3 guna. Beta?

4b + 5 = 3(b + 5) → b = 10.

WHY sahi hai? 40 + 5 = 45 = 3 × 15 ✅

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Example 3 (NCERT style): Karim: kharcha 8, teen chakkar, aakhir 0. Shuru?

8x − 56 = 0 → 7.

WHY sahi hai? Check ✅

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Priya ka mantra: “Kahani padho, x likho, equation banao!” 🎉

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🏠 Real Life Mein

🛒 Dukaan ka munafa: kitne bechein, kis daam pe.
👨‍👩‍👧 Umar ki paheliyaan.
🐔 Kisaan ka hisaab (sir-pair).
💰 Bachat: double hoti rakam aur kharcha.

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🧭 Kab Use Karein, Kab Nahi

Situation	Kya karein	Kyun
Kahani mein anjaan	✅ x maano	Equation banao
Bina letter	✅ “Sab ek jaisa maano” trick	Sir-pair
Har kadam double − c	✅ 2ⁿx − (2ⁿ − 1)c	Karim
Jawab check	✅ Kahani mein wapas daalo	Hamesha

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❌→✅ Worked Mistake

Sawaal: Maa beti ki 5 guna; 6 saal baad 3 guna.

❌ Galat: “5d + 6 = 3d + 6 → d = 0.”

Galti kya hai? 6 saal baad beti bhi d + 6 hogi, uska 3 guna 3(d + 6) ❌

✅ Sahi: 5d + 6 = 3d + 18 → d = 6.

Yaad rakho: Samay sabke liye badhta hai!

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📝 10 MCQs

Q1. Karim shuru?

(a) 7

(b) 8

(c) 56

(d) 14

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Kharcha.
(c) galat: Nahi.
(d) galat: Nahi.

Q2. Ghode (55 sir, 150 pair)?

(a) 20

(b) 35

(c) 40

(d) 15

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Murgiyaan.
(c) galat: Nahi.
(d) galat: Nahi.

Q3. Beti ki umar?

(a) 6

(b) 30

(c) 12

(d) 3

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Maa.
(c) galat: Nahi.
(d) galat: Nahi.

Q4. Gauri ki gaayein?

(a) 6

(b) 12

(c) 3

(d) 9

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Naina.
(c) galat: Nahi.
(d) galat: Nahi.

Q5. Dosa daam (100 dosa, ₹2000 munafa)?

(a) ₹80

(b) ₹70

(c) ₹50

(d) ₹20

Solution dekho

Sahi jawab: (a)

(a) sahi: 8000 ÷ 100 ✅
(b) galat: Laagat bhoole.
(c) galat: Nahi.
(d) galat: Nahi.

Q6. ₹50 pe kitne dosa?

(a) 175

(b) 140

(c) 100

(d) 200

Solution dekho

Sahi jawab: (a)

(a) sahi: 7000 ÷ 40 ✅
(b) galat: 7000 ÷ 50.
(c) galat: Nahi.
(d) galat: Nahi.

Q7. Phool kam se kam?

(a) 7

(b) 8

(c) 14

(d) 1

Solution dekho

Sahi jawab: (a)

(a) sahi: 8x = 7s ✅
(b) galat: Mandir mein.
(c) galat: Nahi.
(d) galat: Nahi.

Q8. (1+3+5)/(7+9+11)?

(a) 1/3

(b) 1/2

(c) 3/7

(d) 3

Solution dekho

Sahi jawab: (a)

(a) sahi: 9/27 = 1/3 ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

Q9. Karim faayde mein kab?

(a) c < x

(b) c > x

(c) c = 8x

(d) Kabhi nahi

Solution dekho

Sahi jawab: (a)

(a) sahi: 8x − 7c > x ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

Q10. Jinn sab le jaaye: c?

(a) 8x/7

(b) x

(c) 8x

(d) 7x/8

Solution dekho

Sahi jawab: (a)

(a) sahi: 8x − 7c = 0 ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Ulta.

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❓ FAQs (Bachchon Ke Asli Sawaal)

1. Equation kaise banaayein?

Anjaan ko x, kahani ko kadam-kadam algebra mein.

2. Bina algebra?

“Sab ek jaisa maano” jaise tricks, ya ulta chalo (aakhir se shuru).

3. Phool ka jawab ek hi?

Nahi, 7k phool, 8k har mandir; sabse chhota 7.

4. Jawab negative aaye?

Kahani mein galti; dobara padho.

5. Check zaroori?

Haan, jawab kahani mein daal ke dekho.

6. Ulta chalna kya?

Karim: aakhir 0 → chakkar 3 se pehle 8 tha (8 ÷ 2 = 4 → +8 …).

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🏋️ Practice Zone (12 Sawaal)

Q1. Easy 2x + 5 = 19?

Solution dekho

Q2. Easy Sir 10, pair 28: ghode?

Solution dekho

Q3. Easy Ram Shyam se 3 guna, jod 48. Shyam?

Solution dekho

12.

Q4. Easy 1/3 pattern ka agla: (1+3+5+7)/(9+11+13+15)?

Solution dekho

16/48 = 1/3.

Q5. Medium Karim kharcha 6, shuru 7. Teen chakkar ke baad?

Solution dekho

56 − 42 = 14 (faayda!).

Q6. Medium Kharcha 10, aakhir 0. Shuru?

Solution dekho

8x = 70 → 8.75 (poora nahi → aisa nahi ho sakta sikkon mein).

Q7. Medium Dosa ₹60 pe ₹2000 munafa: kitne?

Solution dekho

7000 ÷ 50 = 140.

Q8. NCERT style 55 sir, 150 pair, bina letter.

Solution dekho

Sab murgi → 110; 40 ÷ 2 = 20 ghode.

Q9. NCERT style Maa-beti umar.

Solution dekho

6 aur 30.

Q10. Medium Do mandir (phool double, barabar, aakhir 0)?

Solution dekho

4x − 3s = 0 → x = 3, s = 4.

Q11. Medium Naina 2 guna, 5 de to barabar?

Solution dekho

2G − 5 = G + 5 → G = 10.

Q12. NCERT style 1/3 pattern kyun?

Solution dekho

n² ÷ 3n².

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🧠 HOTS (Sochne Wale Sawaal)

Q1. Karim 4 chakkar, kharcha c, aakhir 0. Shuru?

Solution dekho

16x − 15c = 0 → x = 15c ÷ 16.

Q2. Phool 4 mandir?

Solution dekho

16x = 15s → x = 15, s = 16.

Q3. Sir-pair mein pair odd aaye to?

Solution dekho

Mumkin nahi (sab pair even).

Q4. (1+3+…+(2n−1))/(next n odds) hamesha 1/3?

Solution dekho

Haan, n²/3n².

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🏆 Olympiad Corner

Q1. Karim ke 3 chakkar mein kharcha 8, shuru 10. Aakhir?

Solution dekho

80 − 56 = 24.

Q2. Ek number ka 3 guna + 7 = 5 guna − 9?

Solution dekho

2x = 16 → 8.

Q3. Bakriyaan aur batakh: 30 sir, 84 pair. Bakriyaan?

Solution dekho

(84 − 60) ÷ 2 = 12.

Q4. Dosa: laagat ₹12, kiraya ₹4000, daam ₹52. Break-even?

Solution dekho

4000 ÷ 40 = 100 dosa.

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💗 CharuMam Motivation

Karim ne bina soche jinn ki baat maan li aur sab kho diya! 🧞

Koi bhi “double” ka laalach de, pehle hisaab lagao. Algebra sirf kitaab nahi, samajhdaari ka hathiyaar hai! 💡 Chapter poora, badhaai!

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🟢 Master Recap

Kahani → x → equation → jawab → check.
Karim: 8x − 7c; c < x to faayda; c = 8x/7 to sab gaya.
Phool: 8x = 7s → 7 aur 8.
Sir-pair: “sab murgi maano” trick.
1/3 pattern: n² / 3n².

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👉 Aage Kya?

🎉 Chapter 6 poora! Ab Book 2 ka aakhri chapter: Area! 📐

← Pichla: Post 6 — Divisibility Tricks Ka Raaz 📚 Chapter 6 ke saare posts Agla chapter: Area →

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✅ Pehle Yeh Aata Hai?

🎬 Kahani: Karim Aur Jinn

📖 Concept: Kahani Ko Equation Mein Badlo

Step 1: Karim aur jinn

Step 2: Phool aur teen mandir

Step 3: Sir aur pair

Step 4: Umar aur gaayein

Step 5: Dosa ki gaadi

🔐 Deep Concept: 1/3 Ka Chhupa Pattern

✏️ Solved Examples

🏠 Real Life Mein

🧭 Kab Use Karein, Kab Nahi

❌→✅ Worked Mistake

📝 10 MCQs

❓ FAQs (Bachchon Ke Asli Sawaal)

🏋️ Practice Zone (12 Sawaal)

🧠 HOTS (Sochne Wale Sawaal)

🏆 Olympiad Corner

💗 CharuMam Motivation

🟢 Master Recap

👉 Aage Kya?

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